After Ed Miliband stepped down as Labour leader, he led calls within the party to have an open and frank debate about its future. This idea had some merit: Labour had failed to win key marginals across England and Wales, came under serious electoral pressure from UKIP in the north of England, and was all but wiped out in Scotland.

Up stepped Jeremy Corbyn, first elected in 1983 and widely considered a throwback to the once powerful Bennite wing of the party. He has firm anti-austerity views and is explicitly committed to a greater redistribution of wealth funded by higher taxes on business and the affluent. Yet fast forward nearly three months and polling of Labour’s membership is showing that he might actually win. He is seen as different from his competitors, even more so after the recent vote on the welfare bill in which the majority of Labour MPs abstained rather than vote against Tory austerity. Corbyn was the only one of the four leadership candidates to vote against.

His potential victory has provoked fresh warnings from senior Labour figures, most notably Tony Blair, that shifting left may be disastrous for Labour’s electoral chances at the 2020 general election. But where does that leave Scotland? Given that the collapse in the Labour vote north of the border will make it much harder for the party to win UK elections if it becomes permanent, this is suddenly an important question.

Recall that the SNP won 56 of 59 seats in Scotland with a manifesto committed to promoting anti-austerity policies, and that the 45% who voted Yes to independence were more likely to be driven by left-wing ideas than No voters. If Corbyn does win, could the politics he espouses kickstart a revival for the party north of the border?

It is possible to analyse how fertile the electoral ground in Scotland might be for a more left-wing leader of the UK Labour party by looking at the sizeable Scottish sub-sample of the British Election Study. The study includes a left-right scale of voter opinion from five questions on attitudes towards things like redistribution of wealth.

What this revealed about the ideological positioning of Scottish voters at the general election is illustrated in the figure below. The vertical axis measures the percentage of the overall vote share of the party by position on the left-right scale. As we can see, voters of both Labour and the SNP are noticeably skewed towards the left, with almost a quarter of SNP voters on the furthest left position on the scale. In theory, a left-wing candidate such as Corbyn would be well suited to picking up these voters, many of whom have indeed voted Labour in the past.

Ideology of Scottish voters in 2015 election by party choiceBritish Election Study

Yet the constitutional question makes Scottish politics more complex than this. The graphic below shows us the ideology of those who who voted for the SNP in the 2015 election, separating those who voted Yes and No at the independence referendum.

The results show that those who voted SNP and Yes were markedly more left wing than the SNP and No contingent (the Yes SNP voters outnumbered those who voted No and SNP by eight to one). So although there is a huge chunk of the Scottish electorate that appears to be receptive to a more left-wing message, the national dimension of Scottish electoral politics would undoubtedly present Corbyn Labour with a steep mountain to climb given the party’s opposition to Scottish independence.

Given that those SNP voters who voted Yes are more skewed to the left, the potential for Labour to win them back from the left is doubly difficult given that constitutional preferences clearly interact with ideology. It is hard to see how Labour, even with Corbyn at the helm, can outfox the SNP on this crucial issue.

SNP voters’ political bias 2015 by how they voted in the indyrefBritish Election Study

This issue is further highlighted by the graphic below. It shows the ideology of Scottish voters in terms of how happy they were with the referendum result. It clearly illustrates that at least half of those who are most left-wing in Scotland are disappointed by the outcome.

Indeed the more left-wing you are, the more likely you are to be unhappy with the constitutional status quo, and presumably still committed to Scottish independence. Many voters who may well be receptive to Corbyn if they lived in other parts of the UK would therefore be likely to place a lot of blame on Labour for its role in securing a No vote. They are unlikely to be quickly or easily be tempted to vote for the party for the foreseeable future.

Ideology vs reaction to referendum resultBritish Election Study

The election of a left-winger like Corbyn may be a partial solution for Labour in Scotland. From the perspective of left-wing SNP voters, Labour would be seen to be “getting its soul back” and “going back to its roots” in terms of policy. SNP supporters have been having a field day on social media mocking Labour for its mass abstention on the welfare bill, but Corbyn did vote against it and that will mean he will have gained some respect where the other leadership candidates will have certainly lost it.

But the above analysis demonstrates that Labour’s problems in Scotland go far deeper than mere ideological perceptions, with a large group of natural Corbyn supporters apparently likely to be dissuaded by Labour’s position on independence. The conclusion? The stage is set for the SNP to dominate Scottish politics for the foreseeable future, whoever is elected Labour leader.